Week 4 Day 4

Normal distribution (No class meeting)

Learning objectives

• Understand normal distribution is completely determined by its mean and standard deviation
• Define the standardized (Z) score of a data point as the number of standard deviations it is away from the mean: \(Z=(x−\mu)/\sigma\)
• Use the Z score:
  • if the distribution is normal: to determine the percentile score of a data point (using technology or normal probability tables)
  • regardless of the shape of the distribution: to assess whether or not the particular observation is considered to be unusual (more than 2 standard deviations away from the mean)
• Depending on the shape of the distribution determine whether the median would have a negative, positive, or 0 \(Z\) score keeping in mind that the mean always has a Z score of 0.
• Assess whether or not a distribution is nearly normal using the 68-95-99.7% rule or graphical methods such as a normal probability plot.

Checklist

• Finish reading: Chapter 9.5
• Finish watching pre-recorded lecture. You could also find this video on the front page of the course moodle site.
• Finish working on the tutorial exercise and check your answers here.